{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1024ab06",
   "metadata": {},
   "source": [
    "# 高中物理电学公式大全\n",
    "\n",
    "## 1. 静电学\n",
    "\n",
    "### 库仑定律\n",
    "$$ F = k \\frac{q_1 q_2}{r^2} $$\n",
    "$$ k = \\frac{1}{4\\pi\\varepsilon_0} \\approx 9.0 \\times 10^9 {N·m}^2/{C}^2 $$\n",
    "\n",
    "### 电场强度\n",
    "$$ E = \\frac{F}{q} $$\n",
    "$$ E = k \\frac{Q}{r^2} \\quad ({点电荷}) $$\n",
    "\n",
    "### 电场力\n",
    "$$ F = qE $$\n",
    "\n",
    "### 电势能\n",
    "$$ W = qU $$\n",
    "$$ U = k \\frac{q_1 q_2}{r} $$\n",
    "\n",
    "### 电势\n",
    "$$ V = \\frac{W}{q} $$\n",
    "$$ V = k \\frac{Q}{r} \\quad ({点电荷}) $$\n",
    "\n",
    "### 电势差\n",
    "$$ U_{AB} = V_A - V_B = \\frac{W_{AB}}{q} $$\n",
    "\n",
    "### 电场力做功\n",
    "$$ W_{AB} = qU_{AB} = q(V_A - V_B) $$\n",
    "\n",
    "## 2. 恒定电流\n",
    "\n",
    "### 电流强度\n",
    "$$ I = \\frac{q}{t} $$\n",
    "\n",
    "### 电阻定律\n",
    "$$ R = \\rho \\frac{L}{S} $$\n",
    "\n",
    "### 欧姆定律\n",
    "$$ I = \\frac{U}{R} $$\n",
    "\n",
    "### 电功\n",
    "$$ W = UIt = I^2Rt = \\frac{U^2}{R}t $$\n",
    "\n",
    "### 电功率\n",
    "$$ P = UI = I^2R = \\frac{U^2}{R} $$\n",
    "\n",
    "### 焦耳定律\n",
    "$$ Q = I^2Rt $$\n",
    "\n",
    "### 串联电路\n",
    "- 电流：$I = I_1 = I_2 = \\cdots = I_n$\n",
    "- 电压：$U = U_1 + U_2 + \\cdots + U_n$\n",
    "- 电阻：$R = R_1 + R_2 + \\cdots + R_n$\n",
    "\n",
    "### 并联电路\n",
    "- 电压：$U = U_1 = U_2 = \\cdots = U_n$\n",
    "- 电流：$I = I_1 + I_2 + \\cdots + I_n$\n",
    "- 电阻：$\\frac{1}{R} = \\frac{1}{R_1} + \\frac{1}{R_2} + \\cdots + \\frac{1}{R_n}$\n",
    "\n",
    "## 3. 闭合电路欧姆定律\n",
    "\n",
    "### 电动势\n",
    "$$ E = \\frac{W}{q} $$\n",
    "\n",
    "### 闭合电路欧姆定律\n",
    "$$ I = \\frac{E}{R + r} $$\n",
    "\n",
    "### 路端电压\n",
    "$$ U = E - Ir $$\n",
    "\n",
    "### 输出功率\n",
    "$$ P_{{出}} = UI = I^2R $$\n",
    "\n",
    "### 电源效率\n",
    "$$ \\eta = \\frac{P_{{出}}}{P_{{总}}} = \\frac{U}{E} = \\frac{R}{R + r} $$\n",
    "\n",
    "## 4. 电容器\n",
    "\n",
    "### 电容定义\n",
    "$$ C = \\frac{Q}{U} $$\n",
    "\n",
    "### 平行板电容器\n",
    "$$ C = \\frac{\\varepsilon S}{4\\pi kd} $$\n",
    "\n",
    "### 电容器串联\n",
    "$$ \\frac{1}{C} = \\frac{1}{C_1} + \\frac{1}{C_2} + \\cdots + \\frac{1}{C_n} $$\n",
    "\n",
    "### 电容器并联\n",
    "$$ C = C_1 + C_2 + \\cdots + C_n $$\n",
    "\n",
    "### 电容器能量\n",
    "$$ W = \\frac{1}{2}CU^2 = \\frac{1}{2}QU = \\frac{Q^2}{2C} $$\n",
    "\n",
    "## 5. 磁场\n",
    "\n",
    "### 磁感应强度\n",
    "$$ B = \\frac{F}{IL} $$\n",
    "\n",
    "### 安培力\n",
    "$$ F = BIL\\sin\\theta $$\n",
    "\n",
    "### 洛伦兹力\n",
    "$$ F = qvB\\sin\\theta $$\n",
    "\n",
    "### 带电粒子在磁场中运动\n",
    "- 半径：$R = \\frac{mv}{qB}$\n",
    "- 周期：$T = \\frac{2\\pi m}{qB}$\n",
    "\n",
    "## 6. 电磁感应\n",
    "\n",
    "### 法拉第电磁感应定律\n",
    "$$ \\varepsilon = -N\\frac{\\Delta\\Phi}{\\Delta t} $$\n",
    "\n",
    "### 磁通量\n",
    "$$ \\Phi = BS\\cos\\theta $$\n",
    "\n",
    "### 导体切割磁感线\n",
    "$$ \\varepsilon = BLv\\sin\\theta $$\n",
    "\n",
    "### 自感电动势\n",
    "$$ \\varepsilon = L\\frac{\\Delta I}{\\Delta t} $$\n",
    "\n",
    "## 7. 交流电\n",
    "\n",
    "### 正弦交流电\n",
    "$$ i = I_m\\sin(\\omega t + \\varphi) $$\n",
    "$$ u = U_m\\sin(\\omega t + \\varphi) $$\n",
    "\n",
    "### 有效值\n",
    "$$ I = \\frac{I_m}{\\sqrt{2}}, \\quad U = \\frac{U_m}{\\sqrt{2}} $$\n",
    "\n",
    "### 变压器\n",
    "$$ \\frac{U_1}{U_2} = \\frac{n_1}{n_2}, \\quad \\frac{I_1}{I_2} = \\frac{n_2}{n_1} $$\n",
    "\n",
    "### 感抗和容抗\n",
    "- 感抗：$X_L = 2\\pi fL$\n",
    "- 容抗：$X_C = \\frac{1}{2\\pi fC}$\n",
    "\n",
    "## 8. 常用物理常数\n",
    "\n",
    "| 物理量 | 符号 | 数值 |\n",
    "|--------|------|------|\n",
    "| 元电荷 | $e$ | $1.6 \\times 10^{-19}$ C |\n",
    "| 静电力常量 | $k$ | $9.0 \\times 10^9$ N·m²/C² |\n",
    "| 真空介电常数 | $\\varepsilon_0$ | $8.85 \\times 10^{-12}$ C²/N·m² |\n",
    "\n",
    "## 💡 学习要点\n",
    "\n",
    "1. **矢量性**：电场强度、磁感应强度都是矢量\n",
    "2. **叠加原理**：电场、磁场都满足叠加原理\n",
    "3. **能量守恒**：电路中能量守恒是分析问题的基础\n",
    "4. **右手定则**：判断磁场方向、感应电流方向的重要工具\n",
    "\n",
    "## 📝 解题技巧\n",
    "\n",
    "1. 先分析电路结构（串联、并联）\n",
    "2. 明确研究对象和物理过程\n",
    "3. 注意正负号的规定\n",
    "4. 合理选择公式进行计算\n",
    "5. 检查结果的合理性和单位\n",
    "\n",
    "> 掌握这些公式和理解其物理意义是解决电学问题的关键。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "name": "python",
   "version": "3.13.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
